Nuprl Lemma : add-zero-base
∀[x:Base]. x + 0 ~ x supposing (x)↓ ⇒ (x ∈ ℤ)
Proof
Definitions occuring in Statement :
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
add: n + m,
natural_number: $n,
int: ℤ,
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
has-value: (a)↓,
and: P ∧ Q,
top: Top,
implies: P ⇒ Q,
false: False,
prop: ℙ
Lemmas referenced :
add-zero,
base_wf,
equal-wf-base,
is-exception_wf,
has-value_wf_base,
int-value-type,
value-type-has-value,
exception-not-value,
zero-add-sqle,
add-commutes
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
divergentSqle,
callbyvalueAdd,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
thin,
productElimination,
lemma_by_obid,
isectElimination,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination,
voidEquality,
addExceptionCases,
axiomSqleEquality,
independent_isectElimination,
intEquality,
natural_numberEquality,
independent_functionElimination,
exceptionSqequal,
sqleReflexivity,
because_Cache,
sqequalAxiom,
functionEquality
Latex:
\mforall{}[x:Base]. x + 0 \msim{} x supposing (x)\mdownarrow{} {}\mRightarrow{} (x \mmember{} \mBbbZ{})
Date html generated:
2016_05_13-PM-03_29_01
Last ObjectModification:
2016_01_14-PM-06_41_48
Theory : arithmetic
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