Nuprl Lemma : comb_for_eqmod_wf
λm,a,b,z. (a ≡ b mod m) ∈ m:ℤ ⟶ a:ℤ ⟶ b:ℤ ⟶ (↓True) ⟶ ℙ
Proof
Definitions occuring in Statement :
eqmod: a ≡ b mod m,
prop: ℙ,
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
eqmod_wf,
squash_wf,
true_wf,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
Error :universeIsType,
Error :inhabitedIsType
Latex:
\mlambda{}m,a,b,z. (a \mequiv{} b mod m) \mmember{} m:\mBbbZ{} {}\mrightarrow{} a:\mBbbZ{} {}\mrightarrow{} b:\mBbbZ{} {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbP{}
Date html generated:
2019_06_20-PM-02_24_06
Last ObjectModification:
2018_10_03-AM-00_13_05
Theory : num_thy_1
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