recognition /
Complexity /
Complexity.SAT.Backprop /
explainer
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formal statement (Lean)
66 def clauseUnit {n} (σ : PartialAssignment n) (C : Clause n) : Option (Var n × Bool) :=
proof body
Definition body.
67 let vals := C.map (valueOfLit σ)
68 let unknowns := C.zip vals |>.filter (fun ⟨_, o⟩ => o.isNone)
69 if h1 : unknowns.length = 1 then
70 if (vals.filter Option.isSome).all (fun o => o.getD false = false) then
71 let l := unknowns.get ⟨0, by omega⟩
72 match l.fst with
73 | .pos v => some (v, true)
74 | .neg v => some (v, false)
75 else none
76 else none
77
78 /-- A (single) backpropagation step relation with guarded rules. -/
used by (5)
From the project-wide theorem graph. These declarations reference this one in their body.
BPStep
in IndisputableMonolith.Complexity.SAT.Backprop
decl_use
bp_step_sound
in IndisputableMonolith.Complexity.SAT.Backprop
decl_use
clauseUnit_correct
in IndisputableMonolith.Complexity.SAT.Backprop
decl_use
known_lit_false''
in IndisputableMonolith.Complexity.SAT.Backprop
decl_use
xorMissing_correct
in IndisputableMonolith.Complexity.SAT.Backprop
decl_use
depends on (20)
Lean names referenced from this declaration's body.
all
in IndisputableMonolith.Aesthetics.NarrativeGeodesic
decl_use
all
in IndisputableMonolith.Anthropology.KinshipGraphCohomology
decl_use
step
in IndisputableMonolith.Complexity.CellularAutomata
decl_use
Clause
in IndisputableMonolith.Complexity.RSatEncoding
decl_use
PartialAssignment
in IndisputableMonolith.Complexity.SAT.Backprop
decl_use
valueOfLit
in IndisputableMonolith.Complexity.SAT.Backprop
decl_use
Clause
in IndisputableMonolith.Complexity.SAT.CNF
decl_use
Var
in IndisputableMonolith.Complexity.SAT.CNF
decl_use
neg
in IndisputableMonolith.Cryptography.ECDLPWatch
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all
in IndisputableMonolith.Engineering.AsteroidOreSpectroscopy
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neg
in IndisputableMonolith.Foundation.IntegersFromLogic
decl_use
A
in IndisputableMonolith.Foundation.IntegrationGap
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neg
in IndisputableMonolith.Foundation.RationalsFromLogic
decl_use
A
in IndisputableMonolith.Masses.Anchor
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map
in IndisputableMonolith.Measurement.RSNative.Core
decl_use
A
in IndisputableMonolith.Modal.Actualization
decl_use
all
in IndisputableMonolith.Musicology.ModalPreferenceFromPhi
decl_use
neg
in IndisputableMonolith.Numerics.Interval.Basic
decl_use
neg
in IndisputableMonolith.RecogSpec.Core
decl_use
get
in IndisputableMonolith.RRF.Core.Vantage
decl_use