Nuprl Lemma : comb_for_iff_wf
λA,B,z. (A ⇐⇒ B) ∈ A:ℙ ⟶ B:ℙ ⟶ (↓True) ⟶ ℙ
Proof
Definitions occuring in Statement :
prop: ℙ,
iff: P ⇐⇒ Q,
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x]
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
true_wf,
squash_wf,
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
cut,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality
Latex:
\mlambda{}A,B,z. (A \mLeftarrow{}{}\mRightarrow{} B) \mmember{} A:\mBbbP{} {}\mrightarrow{} B:\mBbbP{} {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbP{}
Date html generated:
2016_05_13-PM-03_08_11
Last ObjectModification:
2016_01_06-PM-05_27_44
Theory : core_2
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