Nuprl Lemma : comb_for_remainder_wf
λa,n,z. (a rem n) ∈ a:ℕ ⟶ n:ℕ+ ⟶ (↓True) ⟶ ℕ
Proof
Definitions occuring in Statement :
nat_plus: ℕ+,
nat: ℕ,
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
remainder: n rem m
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
remainder_wf,
squash_wf,
true_wf,
nat_plus_wf,
nat_wf
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
Latex:
\mlambda{}a,n,z. (a rem n) \mmember{} a:\mBbbN{} {}\mrightarrow{} n:\mBbbN{}\msupplus{} {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbN{}
Date html generated:
2019_06_20-PM-01_13_59
Last ObjectModification:
2018_10_03-AM-00_45_32
Theory : int_2
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