Nuprl Lemma : comb_for_wellfounded_wf
λA,r,z. WellFnd{i}(A;x,y.r[x;y]) ∈ A:Type ⟶ r:(A ⟶ A ⟶ ℙ) ⟶ (↓True) ⟶ ℙ'
Proof
Definitions occuring in Statement :
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
prop: ℙ,
so_apply: x[s1;s2],
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
wellfounded_wf,
squash_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
cut,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality
Latex:
\mlambda{}A,r,z. WellFnd\{i\}(A;x,y.r[x;y]) \mmember{} A:Type {}\mrightarrow{} r:(A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbP{}'
Date html generated:
2016_05_13-PM-03_18_26
Last ObjectModification:
2015_12_26-AM-09_06_49
Theory : well_fnd
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